Scomporre i seguenti trinomi caratteristici di secondo tipo:

1) $\displaystyle 10x^2+7x-6=$

$\displaystyle = 10x^2-5x+12x-6=$

$\displaystyle =5x(2x-1)+6(2x-1)=$

$\displaystyle =(2x-1)(5x+6)$.

2) $\displaystyle 3t^2+14-5=$

$\displaystyle =3t^2-1t+15t-5=$

$\displaystyle =t(3t-1)+5(3t-1)=$

$\displaystyle =(3t-1)(t+5)$.

3) $\displaystyle 6u^2+5u-6=$

$\displaystyle = 6u^2+9u-4u-6=$

$\displaystyle =3u(2u+3)-2(2u+3)=$

$\displaystyle =(2u+3)(3u-2)$.

4) $\displaystyle 2x^2+x-28=$

$\displaystyle =2x^2+8x-7x-28=$

$\displaystyle =2x(x+4)-7(x+4)=$

$\displaystyle =(x+4)(2x-7)$.

5) $\displaystyle 15p^2+7p-2=$

$\displaystyle =15p^2+10p-3p-2=$

$\displaystyle =5p(3p+2)-(3p+2)=$

$\displaystyle =(3p+2)(5p-1)$.

6) $\displaystyle 2x^2-5ax-3a^2=$

$\displaystyle =2x^2-6ax+ax-3a^2=$

$\displaystyle =2x(x-3a)+a(x-3a)=$

$\displaystyle =(x-3a)(2x+a)$.

7) $\displaystyle 9x^2-6ax-8a^2=$

$\displaystyle =9x^2-12ax+6ax-8a^2=$

$\displaystyle =3x(3x+2a)-4a(3x+2a)=$

$\displaystyle =(3x+2a)(3x-4a)$.

8) $\displaystyle 2x^2-9ax-5a^2=$

$\displaystyle =2x^2-10ax+ax-5a^2=$

$\displaystyle =x(2x+a)-5a(2x+a)=$

$\displaystyle =(2x+a)(x-5a)$.